Order of Operations

The fundamental concept behind the order of operations is to perform arithmetic operators in the “right” order or sequence. Let’s take a look at how Rob and Patty tried to simplify a given numerical expression by applying the order or rule of operations.

What is Rob’s mistake?

He carelessly simplified the numerical expressions by applying arithmetic operations from left to right.

Patty got the correct answer because she properly applied the rules on order of operations.

She performed multiplication and division first before addition and subtraction.

To avoid different answers like what happened to Rob and Patty, mathematicians decided to agree on specific rules and procedures to follow in simplifying or calculating numerical expressions. That day, the Order of Operations or PEMDAS rule was created…

What is the Order of Operations?

The order of operations or PEMDAS is merely a set of rules that prioritize the sequence of operations starting from the most important to the least important.

Step 1: Do as much as you can to simplify everything inside the parenthesis first

Step 2: Simplify every exponential number in the numerical expression

Step 3: Multiply and divide whichever comes first, from left to right

Step 4: Add and subtract whichever comes first, from left to right

Examples on How to Apply the Order of Operations to Simplify Numerical Expressions

The next examples will now involve parentheses. Remember that you have to simplify everything inside the parenthesis first before going forward. The rules for order of operations apply the same way inside the parenthesis.

The final examples will involve exponents so be careful with each step because they are so many things going on. As long as you remain focus in following the rules governing the order of operations, it shouldn’t be that difficult! Here we go…

Example 5: Simplify 24−5(10−42 ÷ 2) + (30−33) using PEMDAS rule.

Simplify the expressions inside the parentheses and the exponential numbers first.